There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{x{(1 - {x}^{2})}^{1}}{2} + {e}^{(2x - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-1}{2}x^{3} + \frac{1}{2}x + {e}^{(2x - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-1}{2}x^{3} + \frac{1}{2}x + {e}^{(2x - 1)}\right)}{dx}\\=&\frac{-1}{2}*3x^{2} + \frac{1}{2} + ({e}^{(2x - 1)}((2 + 0)ln(e) + \frac{(2x - 1)(0)}{(e)}))\\=&\frac{-3x^{2}}{2} + 2{e}^{(2x - 1)} + \frac{1}{2}\\ \end{split}\end{equation} \]

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